Really hoping someone can help me with this.

I just recently moved to Redwood City in CA and found that my location has a lot of consistent traffic of big rigs. Some of them pause right next door to drop off my neighbor. They chat, and I inhale the wonderful exhaust.

The property isn't too large, and I'm planning on tearing out the overgrown lawn and growing veggies and pretty inedible things. The front yard is the only yard I have, otherwise I'd grow the edibles in the back. Good news is that there's a good 6' or so fence around the entire property.

Now, the trees. There are about five or six trees on the property and a enormous mess of maybe three trees growing on top of each other right outside of the fence, but probably still within property lines. BF wants all the trees taken down. There's:

A mature and very tall holly tree at the back corner of the house that doesn't seem to be damaging the foundation.

A plum (?) tree, also very mature, leaning over into the property so that we think the roots might have extended into the neighbor's property and may potentially harm their foundation.

A mature citrus tree (maybe orange?) that is lifting the bricks in the yard.

A deciduous-looking tree next to the house that has already damaged the foundation causing one of the bedroom floor corners to tilt ever-so-slightly downwards.

A bottlebrush tree.

And finally the clump outside the fence looks like three trees were planted in the same very small plot. I can't identify two of them, and the type of the third one escapes me right now. The description that comes to mind is something like a Jurassic Palm.

All of the trees are in desperate need of pruning and are more than one-story high. I don't like the Holly or the Bottlebrush.

I'm wondering about general input about taking these trees down. How hard it is, whether or not it is worth it to pay someone, or maybe if we shouldn't take them down at all for whatever reason.

The part I'm most concerned about is this: if I take down the trees, there is nothing between the Budweiser logistics building and all their trucks, and myself and my garden. I want to put trees back up if we take those down. Can someone offer suggestions for a few pretty looking and low maintenance (as far as pruning goes- unless it's really pretty, then I'll just have to learn to prune LOL) trees that that easygoing root systems and will grow quickly enough to spare my garden's air? I want to be considerate of my neighbor- otherwise I wouldn't care how crazy the roots go or if it sheds like crazy and sticks branches all over their driveway.

Thanks in advance. Sorry I tend to go on and on...